Question 6.

Area of a regular hexagon = $\frac{3\sqrt{3}}{2}x^2$

Area of an equilateral triangle = $\frac{\sqrt{3}}{4}(a)^2$ ; where $a =$ side of the triangle

Since the area of the two figures are equal, we can equate them as follows:

$\frac{3\sqrt{3}}{2}x^2 = \frac{\sqrt{3}}{4}(12)^2$

On simplifying: $x^2 = 24$

$x = 2\sqrt{6}$